Seismic data acquisition using designed non-uniform receiver spacing

ABSTRACT

The presently disclosed technology relates to an arrangement for seismic acquisition where the spacing between adjacent pairs of receiver and sources lines is not all the same. Some receiver and/or source lines and/or receiver and/or source spacings are larger and some are smaller to provide a higher quality wavefield reconstruction when covering a larger total area or for a similar total area of seismic data acquisition, while providing a wavefield that is optimally sampled by the receivers and sources so that the wavefield reconstruction is suitable for subsurface imaging needs.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/809,838, filed Nov. 10, 2017, which is a continuation of U.S. patentapplication Ser. No. 13/156,104, filed Jun. 8, 2011, now U.S. Pat. No.9,846,248, which claims priority to U.S. Provisional Application Nos.61/353,095 and 61/353,089, both of which were filed on Jun. 9, 2010.Each of these applications is incorporated by reference in its entiretyherein.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

None.

FIELD OF THE INVENTION

This invention relates to seismic data acquisition of geologicstructures in the earth and processing the data that is useful ininterpreting the geologic structures.

BACKGROUND OF THE INVENTION

Seismic data is acquired to investigate and map the structures andcharacter of geological formations under the earth. Seismic data istypically gathered by laying out seismic receivers (e.g., geophones orsimilar sensors) in a survey area and directing one or more seismicsources such as vibrator trucks to move from shot point to shot pointand direct seismic energy into the ground. As the seismic sources directseismic energy into the earth where they are reflected and/or refractedby interfaces between subsurface geological formations the seismicreceivers sense the resulting reflected and/or refracted energy, therebyacquiring seismic data that provides information about the geologicalformations under the ground. Basically a seismic source emits awavefield that propagates down through the earth and is reflected and/orrefracted by interfaces between subsurface geological formations thenpropagates back to the surface where the receivers detect and discretelysample the returning, ascending or upcoming wavefield.

Typically, thousands of discrete seismic receivers are used to gatherseismic data. The seismic receivers are generally laid out in lines thatare substantially parallel and laterally spaced at equal distances anduniformly spaced down the line. In this configuration, uniform coverageof the subsurface is achieved. It is conventional that receiver spacingalong the lines is closer than the spacing between the lines and that,therefore, the wavefield detected by the sensors is less well sampled inthe lateral direction (perpendicular to the receiver lines) in mostseismic surveys. The normal ratio of the station spacing to the linespacing runs between 2 and 30 to 1. This means that the spacing of thereceivers along the line is between half and one thirtieth the spacingbetween parallel receiver lines. This is normally due to the costs andexpense of adding additional receiver lines that can dramaticallyincrease the expense of the survey to achieve a better sampling of thereturning, ascending or upcoming wavefield.

SUMMARY OF THE INVENTION

The invention more particularly includes a method of acquiring seismicdata including deploying receivers in a survey area where each receiveris laterally spaced from one another in two horizontal directionswherein the lateral spacing in at least one horizontal direction isdeliberately non-uniform and wherein the spacing between any two seismicreceivers in the deliberately non-uniform direction varies by a distanceof at least five percent between the largest spacing and smallestspacing. The method further includes directing seismic energy into theground and recording reflected and/or refracted seismic data with thedeployed seismic receivers, recovering the measured data from thedeployed seismic receivers, and reconstructing the wavefield from therecovered data.

The invention also relates to a method of acquiring seismic dataincluding deploying receivers in a survey area and identifying seismicsource points within the survey area where each source point islaterally spaced from one another in two horizontal directions whereinthe lateral spacing in at least one horizontal direction is deliberatelynon-uniform and wherein the spacing between any two seismic sourcepoints in the deliberately non-uniform direction varies by a distance ofat least five percent between the largest spacing and smallest spacing.The method further includes directing seismic energy into the ground atthe source points and recording reflected and/or refracted seismic datawith the deployed seismic receivers, recovering the measured data fromthe deployed seismic receivers, and reconstructing the wavefield fromthe recovered data.

A particular preferred embodiment of the present invention relates to amethod of acquiring seismic data including deploying receivers in asurvey area where each receiver is laterally spaced from one another intwo horizontal directions and identifying source points wherein eachsource point is laterally spaced from one another wherein the lateralspacing for each of the source points and for each of the receivers isdeliberately non-uniform in at least one horizontal direction andwherein the horizontal spacing between any two seismic receivers in thedeliberately non-uniform direction varies by a distance of at least fivepercent between the largest spacing and smallest spacing and furtherwherein the horizontal spacing between any two seismic source points inthe deliberately non-uniform direction varies by a distance of at leastfive percent between the largest spacing and smallest spacing. Themethod further includes directing seismic energy into the ground fromthe source points and recording reflected and/or refracted seismic datawith the deployed seismic receivers, recovering the measured data fromthe deployed seismic receivers, and reconstructing the wavefield fromthe recovered data.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention, together with further advantages thereof, may best beunderstood by reference to the following description taken inconjunction with the accompanying drawings in which:

FIG. 1 is schematic top view of a portion of a seismic survey areashowing a conventional arrangement of lines of seismic receivers withshot points;

FIG. 2 is schematic top view of a portion of a seismic survey areashowing one inventive arrangement of lines of seismic receivers withshot points;

FIG. 3 is schematic top view of a portion of a seismic survey areashowing a second inventive arrangement of lines of seismic receiverswith shot points;

FIG. 4 is schematic top view of a portion of a seismic survey areashowing a third alternative inventive arrangement of lines of seismicreceivers with shot points;

FIG. 5 is schematic top view of a portion of a seismic survey areashowing a fourth alternative inventive arrangement of lines of seismicreceivers with shot points;

FIG. 6 is schematic top view of a portion of a seismic survey areashowing a fifth alternative inventive arrangement of lines of seismicreceivers with variably spaced shotpoints;

FIG. 7 is a is schematic top view of a portion of a seismic survey areashowing a sixth alternative inventive arrangement of lines of seismicreceivers with shot points;

FIG. 8 is schematic top view of a portion of a seismic survey areashowing a seventh alternative inventive arrangement of lines of seismicreceivers with shot points;

FIG. 9 is schematic top view of a portion of a seismic survey areashowing an eighth alternative inventive arrangement of lines of seismicreceivers with shot points;

FIG. 10 is schematic top view of a portion of a seismic survey areashowing a ninth alternative inventive arrangement of lines of seismicreceivers with shot points; and

FIG. 11 is schematic top view of a portion of a seismic survey areashowing a tenth alternative inventive arrangement of lines of seismicreceivers with shot points.

DETAILED DESCRIPTION OF THE INVENTION

Turning now to the preferred arrangement for the present invention,reference is made to the drawings to enable a more clear understandingof the invention. However, it is to be understood that the inventivefeatures and concept may be manifested in other arrangements and thatthe scope of the invention is not limited to the embodiments describedor illustrated. The scope of the invention is intended only to belimited by the scope of the claims that follow.

An exemplary conventional seismic data acquisition system is indicatedby the arrow 10 in FIG. 1. The seismic data acquisition system 10comprises lines of receivers where eight such lines are shown andlabeled 15A, 15B, 15C, 15D, 15E, 15F, 15G and 15H. The receiver linesare arranged substantially parallel to one another and are commonlyspaced a common and uniform distance apart. Along each receiver line area number of generally evenly spaced receivers 17, indicated by “x's”.Also shown with small circles are shot points 18 at which the seismicsources would generate and direct seismic energy into the ground. Asarranged, the total system width of the system 10 is S₁. The width-wiseor lateral receiver line spacing between each adjacent pair of receiverlines is one seventh of S₁ and indicated as 19 _(ab), 19 _(bc), 19_(cd), 19 _(de), 19 _(ef), 19 _(fg) and 19 _(gh). In FIG. 1, thereceiver line spacing is such that nominally:

19 _(ab)=19 _(bc)=19 _(cd)=19 _(de)=19 _(ef)=19 _(fg)=19 _(gh).

In accordance with the present invention, it has been found that even orequal receiver line spacing may not be most optimal for acquiringseismic data. Noise in the data set may be most readily identified byeven spacing and therefore fairly easily filtered or cancelled inpost-acquisition processing. But highly non-uniform or irregular spacingmay actually provide better results in general. Additionally it has beenfound that the wavefield sensed in the lateral dimension (perpendicularto the receiver lines) by the receivers can be better and moreaccurately reconstructed if the receivers are spaced in a highlynon-uniform or irregular spacing.

The reason for this is the method of wavefield sampling. A uniform gridor series of lines is much like a tree farm with trees neatly laid outin rows with a common, but close spacing of each tree within a row. Thegaps between the trees represent gaps in seismic data that are literallylarge enough to drive a tractor through it. We don't know what is in thegaps and since they extend so far, there may be something fairly large.However, where the trees are lined up, the seismic data is oversampledas a recorder may actually be turned off and the two adjacent receiverswill almost certainly provide sufficient data to accurately predict whatthe silent recorder would have captured. What should be disturbing isthat the gaps are not just between two rows, but there are gaps runningat 45 degree angles and 90 degree angles to the rows. Consider the viewswithin Arlington National Cemetery where one is seeing all of theheadstones that are perfectly aligned. Many headstones are somewhathidden by the perfect alignment in quite a few orientations. Thisarrangement of headstones is good for demonstrating military precisionand honoring fallen soldiers, but not as good for getting as muchinformation about the geologic subsurface with the receivers available.While a random arrangement of receivers or sources is not desired, thepoint of a desired non-uniform arrangement may be visualized whilestanding in the middle of a dense forest where one has the impression ofseeing an impenetrable array of trees. From any location, there areenough trees in view to be seen in a composite as an impenetrableforest. In a tree farm that may actually have more trees than the forestallows long views that are wide enough for tractors to easily drive. Therows of trees make the hidden trees seem redundant.

The critical question is how variable can we space the lines andstations and still recover our wavefield accurately. With knowledge ofthe likely complexity of the subsurface, synthetic surveys may beconstructed and run on computers using varying arrays of receivers andsources. Using the data acquired by the synthetic survey, a wavefieldreconstruction is created and compared to the underlying model. Avariety of such tests will provide guidance to designing the variousspacings in the actual survey. Clearly, a sparser survey is a lessexpensive survey and if accuracy can be obtained at lower cost, then asparser survey will be undertaken that will provide the accuracy orprecision needed.

Essentially, geophysicists are able to process and interpret seismicdata to map the various interfaces between formations based onindividual data points established by the time delay of the signalreturned from the formation. The data actually forms a large pluralityof interface points. The points may be seen to form a nearly continuousline along each of the interfaces in the direction of the vessel travel.Closely spaced “lines” of receivers provides higher three dimensionaldefinition, but at considerably higher cost. Simply put, it takes acertain amount of time to deploy a line of seismic receivers and recoverit from the field. Therefore, close lateral spacing of receiver linesmeans more labor cost and time performing the survey. While it would bepreferred to properly sample the wavefield containing the echo returnswith close spacing of lines and receivers, the costs associated withsuch a proper survey can be very costly to cost prohibitive.

Currently, geoscientists interpolate the shape of the geologicalinterfaces in the gaps between points by using the data received byseismic receivers that are close to the gaps in question. Mostinterpolation algorithms are simple mathematical processes, such asbasic averaging of the nearby data. With the missing informationsupplied by the interpolation, the data is provided to seismicprocessors to create an image of the geological subsurface. However,according to the present invention, it is better to reconstruct theentire wavefield in one realization. Wavefield reconstruction involvesstatistical linear regression analysis where a model wavefield iscreated from prior knowledge of the geological subsurface and isiteratively refined based on actual measured data from the seismicsurvey. Through the regression analysis, the L0 and L1 norms arecalculated for each comparison between the model wavefield and theactual data such that the model wavefield is iteratively corrected untilcalculated L0 and L1 norms are minimized. At L0 and L1 normminimization, the model wavefield is believed to most accuratelyrepresent the actual wavefield that would have ascended from thegeological subsurface if data could have been recorded at every possiblelocation. Thus, at this point, the model wavefield or reconstructedwavefield may provide data from the entire surveyed area including allgaps between points and from any point or points within the survey area.Data from the reconstructed wavefield is then processed in theconventional manner to create a three dimensional image of thesubsurface structures. With an accurately reconstructed wavefield, theshape of the geological interfaces can be more properly imaged. Itshould be recognized that wavefield reconstruction utilizes data fromreceivers well distant from gaps as the iterative process attempts to“fit” the model wavefield to the larger data set. Wavefieldreconstruction algorithms model the wavefield based upon its componentsand the physical properties of the survey area being sampled. In thepresent invention, prior knowledge of the geological substructures inthe design of the receiver array and especially the non-uniform spacingof the receiver array enhances and enlarges the strength of suchalgorithms to obtain a more accurate reconstructed wavefield with thesame number or fewer data points. Wavefield reconstruction also takesadvantage of the truism that the simplest model of the earth thataccurately fits the measured data is likely the most correct model.Thus, by minimizing the L0 and L1 norms, the complexity of the geologicmodel that accurately matches the measured data is also minimized andprovides a very useful reconstructed wavefield for imaging.

The wavefield reconstruction fidelity is dependent on the receiverspacings used in the sampling of the wavefield. It has been found thatthe wavefield sensed in the lateral dimension (perpendicular to the lineof receivers) by the receivers can be better reconstructed if thereceivers are spaced in a non-uniform or irregular spacing. Theestimation can typically be quite accurate depending on the complexityof the geological interface. A flat interface is quite easy.

Consider the situation where someone desires to determine the contour ofthe bottom of a back yard pond where the water is dark and the persondoes not want to get wet. Since we know beforehand that a pool normallyhas a generally flat or rounded bottom with some small variation indepth from one end to the other and that the deepest points will be awayfrom the edges and somewhere centered within the pool, we can use thisknowledge to take some short cuts. Using this knowledge, we candetermine that a solution would be to take a yard stick and dip it intothe pond at various places in the pond and develop a rough, but fairlyaccurate model of the bottom of the pond. This use of prior knowledge ofthe general type and nature of the pool allows us to model the problemand determine a method that would sample less densely and just a fewprofiles allow us to determine a very accurate representation of thepool bottom.

Next, let us consider what would happen if the pool is now a murkyfishing pond. Now we cannot make the assumption that the pool bottom isflat or smooth in fact more than likely the bottom is quite rough withrocks logs and other trash. If we look around the area on the surface wemight conclude the bottom could have logs, brush or rocks. In this case,if the bottom is a very rough surface or unpredictable surface, thecontour of the bottom is much more complicated and challenging to surveywith few samples. Now a more densely sampled survey with more samplingprofiles would be needed to accurately measure the subsurface. This kindof complication routinely occurs in seismic surveys.

The present invention uses some relatively simple logic to providequality subsurface maps, models or images of geological interfaces, butcreates such maps, models or images from data that can be acquired in amore efficient manner than current techniques using interpolationmethods that are currently available. Returning to the backyard fishingpond example, the present invention would be practiced in a very smallscale but analogous example where the surveyor would make several depthmeasurements fairly close together to determine how smooth or continuousthe bottom is. The surveyor would then combine this knowledge with areview of the observations from the surface and determine the likelihoodof debris and logs or rocks in the pond. If the bottom were to be smoothor flat, then the remainder of the measurements may be few and spreadout. The depth between actual measurements may be confidentlyinterpolated. For example, the depth at a point half way between twoactual measurements two feet apart that are 16 inches and 18 inches maybe confidently interpolated to be 17 inches. One need NOT make theactual measurement, especially if the time or cost to make suchmeasurement is substantial. On the other hand, an efficient surveydesign could be developed that would provide a reasonably accurate modelof a more complicated bottom structure, but the measurements would becloser together. The critical difference is between the concepts ofinterpolation and reconstruction. Interpolation is a mathematicalprocess that does not use prior knowledge of what is being sampled tocalculate the new value. In our example, most algorithms will come upwith 17 inches regardless of the subsurface because that is the averageof the two measurements. Interpolation takes no account of the priorknowledge of what is being sampled. This works with a pool bottom thatis smoothly varying but if we consider a rough bottom of brush, rocksand logs, then we cannot confidently interpolate the answer. In thiscase we must reconstruct the bottom through using prior knowledge of thelikeliness of the roughness on the bottom and proper sampling of thedata we do sample.

Back to a seismic survey, applying the aforementioned concept becomesmuch more complicated for seismic data acquisition in that portions ofthe survey area may be simpler geological structures and other portionsmay have more complicated structures. Typically, a seismic data surveywill survey an area where some data has already been collected, but thedata is not sufficiently rich to resolve potential hydrocarbon depositsfor drilling. This data from prior surveys maybe sparse 3D or 2D seismicdata or even from well logs or other geological observations. Data fromprior surveys may provide enough information to determine the complexityof the geological structures and create models of the substructuressufficient to analyze the “spacing” of actual data necessary to get asufficiently accurate image of the geological substructures that aresufficient to justify the risk for spending millions of dollars onexploration wells. So, this invention is about getting sufficientvolumes or density of seismic data to decide and plan a drilling programwhile minimizing the cost of gathering the seismic data.

Referring now to FIG. 2, a seismic data acquisition system is indicatedby the arrow 20 where eight receiver lines comparable to the eightreceiver lines of FIG. 1. However, the receiver lines 25A, 25B, 25C,25D, 25E, 25F, 25G and 25H are arranged to be spaced from one another byan uncommon or irregular spacing. Along each receiver line are a numberof generally evenly spaced seismic receivers 27. As deployed for seismicdata collection in FIG. 2, the total system width S₂, is wider than S₁.As with system 10 in FIG. 1, each pair of receiver lines have anindividual receiver line spacing indicated as 29 _(ab), 29 _(bc), 29_(cd), 29 _(de), 29 _(ef), 29 _(fg) and 29 _(gh). While one or morereceiver line spacings may be the same as other receiver line spacings,not all are the same. Preferably, at least one receiver line spacing 29is equal to or less that the receiver line spacing 19 of the system 10shown in FIG. 1. Specifically, spacing 29 _(cd) is the same as spacing19 _(cd) while spacing 19 _(ab) is slightly larger than spacing 19 _(ab)and spacing 29 _(bc) is quite a bit larger than spacing 19 _(bc). Atleast one receiver line spacing must be less than or equal to or veryclose to equal to the receiver line spacing 19 of the System 10 in FIG.1 in order to provide the accuracy of the data collected by inventivesystem 20. Since S₂ is wider than S₁, the area to be surveyed will besurveyed in less time at lower cost with an inventive system 20configuration as compared to a conventional system 10 configuration asthe survey area will be covered by fewer receiver lines overall. Therange at which a configuration may be made wider without losingcomparable accuracy depends on the complexity of the subsurfacestructures in the area to be surveyed. Based upon current studies,comparable accuracy may be obtained with S₂ being 10 to 20 percent widerand current estimates are that 35% wider provides data that isaccurately processable. The same current analysis indicates that above35% may create unacceptable holes in the data in certain complexsubstructures, but upwards of 50% and as high as 90% is possible andlikely in fairly simple geologic structures and in seismically benignareas.

Turning now to FIG. 3, the inventive technique of the present inventionmay be used to another and perhaps opposite end. The first end was tocreate an accurate model of the geological substructures with a sparserarray of receiver lines. The opposite end is to provide a much moreprecise model of the geological substructures without giving upproductivity. In FIG. 3, a system 30 is shown where eight receiver linescomparable to the eight receiver lines of FIG. 1 and of FIG. 2. Likesystem 20, the receiver lines 35A, 35B, 35C, 35D, 35E, 35F, 35G and 35Hare arranged to be spaced from one another and by an uncommon orirregular spacing. However, the lateral width S₃ of system 30 isapproximately the same as S₁, the width of conventional system 10. Alongeach receiver line is a number of generally evenly spaced seismicreceivers 37. Like in System 10 in FIG. 1, each pair of receiver lineshave an individual receiver line spacing indicated as 39 _(ab), 39_(bc), 39 _(cd), 39 _(de), 39 _(ef), 39 _(fg) and 39 _(gh). While one ormore receiver line spacings may be the same as other receiver linespacings, not all are the same. Preferably, at least one receiver linespacing 39 is less that the receiver line spacing 19 of system 10 shownin FIG. 1 while one or more receiver line spacings 39 are larger thanthe common receiver line spacing 19. However, since S₃ is essentiallythe same as S₁, the area to be surveyed will take about the same numberof receiver lines and about the same amount of time with the inventivesystem 30 configuration as compared to the conventional system 10configuration. What is key is that having one or two or three receiverline spacings 39 being less than the common receiver line spacing 19provides greater wavefield reconstruction accuracy. The closely spacedreceiver line spacings 39 _(ab) and 39 _(ef) provide accurate data andprovide details for the wavefield reconstruction algorithms andprocessors to more accurately estimate the shape of the geologicalinterfaces in the larger gaps represented by spacings 39 _(bc) and 39_(de). System 30 essentially provides higher detail without higher cost.

In other more preferred embodiments, the receivers themselves do nothave to be equally spaced along the receiver lines. As shown in FIGS. 4and 5, the receiver lines are unequally spaced in the same manner andspacing as system 20 in FIG. 2. In FIG. 4, the system 40 the spacing ofthe receivers along a receiver line is shown to be non-uniform. Itshould be seen that all of the receiver lines have the same common, butunequal spacing. Thus, the receivers are all in common lines or straightcolumns from top to bottom of the drawing. In FIG. 5, the system 50 hasthe same non-uniform receiver line spacing as system 20 in FIG. 2, butthe spacing of the receivers along the receiver line is not onlynon-uniform, but not the same from receiver line to receiver line. Inother words, the receivers do not line up in straight columns.

In FIG. 6, the system 60 does not include alignment in any direction andare two dimensionally non-uniform. It should be noted that the sourcesthrough all of the embodiments from system 20 to system 60 includesources that have been maintained in common regular spacing. Referringto FIG. 7, the system 70 at first appears to be exactly the same assystem 20. All of the receivers are aligned and ordered in the samecommon spacing. However, a closer inspection reveals that the centercolumn of sources are closer to the left column and further from theright column. Essentially, system 70 shows that the sources may also bearranged in the non-uniform arrangements of the receivers.

Referring to FIG. 8, the next level of complication of source spacing isdemonstrated by system 80 which includes varied spacing vertically, butall columns have the same non-uniform spacing.

Referring to FIG. 9, system 90 shows a slightly more complicatedarrangement for the sources where they remain in straight columns, butthe columns are non-uniformly spaced, the spacing vertically within thecolumns is no-uniform and each column is differently non-uniformlyspaced.

System 100 in FIG. 10 shows an additional bit of complexity where thesources are fully varied in both vertically and horizontally in theFigure, but on the ground in both the x and y directions.

What should be recognized in systems 70 through 100 is that thereceivers have all be uniform in both directions. Many combinations ofnon-uniform spacings for both the sources and receivers are possible.The permutations of a few combinations of spacings for both sources andreceivers have been described above. The most complicated combination isshown in FIG. 11 where system 110 includes the sources have full twodimensional non-uniformity and the receivers being fully non-uniform intwo dimensions. The following table suggests that more combinations arepossible and is presented to avoid presenting many extra drawings thatare unnecessary to the understanding of the present invention:

FIG. Source Receiver Prior Art Uniform Uniform FIG. 1 FIG. 2 - widerUniform Non-Uniform LINES with uniform spacing along lines FIG. 3 - highUniform Non-Uniform LINES definition with uniform spacing along linesFIG. 4 Uniform Non-Uniform LINES with REGULAR Non- Uniform spacing alonglines FIG. 5 Uniform Non-Uniform LINES with Irregular Non- Uniformspacing along lines FIG. 6 Uniform Non-Uniform in 2D FIG. 7 Non-UniformLINES with Uniform uniform spacing along lines Non-Uniform LINES withNon-Uniform LINES uniform spacing along with uniform lines spacing alonglines Non-Uniform LINES with Non-Uniform LINES uniform spacing alongwith REGULAR Non- lines Uniform spacing along lines Non-Uniform LINESwith Non-Uniform LINES with uniform spacing along Irregular Non-Uniformlines spacing along lines Non-Uniform LINES with Non-Uniform in 2Duniform spacing along lines FIG. 8 Non-Uniform LINES with UniformREGULAR Non-Uniform spacing along lines Non-Uniform LINES withNon-Uniform LINES REGULAR Non-Uniform with uniform spacing spacing alonglines along lines Non-Uniform LINES with Non-Uniform LINES with REGULARNon-Uniform REGULAR Non-Uniform spacing along lines spacing along linesNon-Uniform LINES with Non-Uniform LINES with REGULAR Non-UniformIRRegular Non-Uniform spacing along lines spacing along linesNon-Uniform LINES with Non-Uniform in 2D REGULAR Non-Uniform spacingalong lines FIG. 9 Non-Uniform LINES with Uniform Irregular Non-Uniformspacing along lines Non-Uniform LINES with Non-Uniform LINES IrregularNon-Uniform with uniform spacing spacing along lines along linesNon-Uniform LINES with Non-Uniform LINES Irregular Non-Uniform withREGULAR Non- spacing along lines Uniform spacing along lines Non-UniformLINES with Non-Uniform LINES Irregular Non-Uniform with Irregular Non-spacing along lines Uniform spacing along lines Non-Uniform LINES withNon-Uniform in 2D Irregular Non-Uniform spacing along lines FIG. 10Non-Uniform in 2D Uniform Non-Uniform in 2D Non-Uniform LINES withuniform spacing along lines Non-Uniform in 2D Non-Uniform LINES withREGULAR Non- Uniform spacing along lines Non-Uniform in 2D Non-UniformLINES with Irregular Non- Uniform spacing along lines FIG. 11Non-Uniform in 2D Non-Uniform in 2D

The ability to adequately reconstruct the wavefield will then depend onthe design of the source and receiver spacings in both dimensions. Caremust be taken in designing such a configuration so that the wavefielddoes not become under sampled for the subsurface objective being imaged.This can be modeled prior to acquisition of the survey to determine therequired station and line spacing.

It should also be understood that receiver lines and source lines maystill be implanted with varying degrees of freedom, but noting thatthere are no particular requirement that the orientation of the sourceline and receiver lines be orthogonal for the wavefield reconstructionto work. The lines may be oriented with variations in direction,patterns or layout. Some of the more common in the industry are thebrick, zig-zag, slash and inline survey designs. Non-uniform line andstation spacing for wavefield reconstruction work equally well with eachof these survey technique.

Finally, the scope of protection for this invention is not limited bythe description set out above, but is only limited by the claims whichfollow. That scope of the invention is intended to include allequivalents of the subject matter of the claims. Each and every claim isincorporated into the specification as an embodiment of the presentinvention. Thus, the claims are part of the description and are afurther description and are in addition to the preferred embodiments ofthe present invention. The discussion of any reference is not anadmission that it is prior art to the present invention, especially anyreference that may have a publication date after the priority date ofthis application.

1. A method of characterizing a geological subsurface, the methodcomprising: designing a seismic survey for a survey area including thegeological subsurface by selecting a plurality of positions within thesurvey area at which to place a plurality of seismic receivers in adeliberately non-uniform arrangement, the plurality of positionsincluding a first position for a first seismic receiver, a secondposition for a second seismic receiver, and a third position for a thirdseismic receiver, the plurality of positions of the deliberatelynon-uniform arrangement selected, such that: the first position for thefirst seismic receiver is not aligned along a first direction with thesecond position for the second seismic receiver, the first position forthe first seismic receiver is not aligned along a second direction withthe third position for the third seismic receiver, and the plurality ofpositions for the plurality of receivers has a deliberately non-uniformspacing between pairs of adjacent receivers in at least one of the firstdirection or the second direction; and wherein the seismic surveyincludes the plurality of seismic receivers at the plurality ofpositions within the survey area, such that seismic data is obtainablebased on seismic energy detected by the plurality of seismic receiversaccording to the seismic survey, the geological subsurface characterizedbased on the seismic data.
 2. The method of claim 1, wherein thedeliberately non-uniform spacing is two-dimensionally non-uniform. 3.The method of claim 1, wherein the seismic survey further includes: thefirst seismic receiver and the second seismic receiver within a samereceiver line; and the third seismic receiver within a differentreceiver line, such that the seismic survey includes the plurality ofseismic receivers being positioned within the survey area in thedeliberately non-uniform arrangement, the deliberately non-uniformarrangement including the plurality of receivers being not alignedwithin the same receiver line and the plurality of receivers being notaligned between the same receiver line and the different receiver line.4. The method of claim 3, wherein the seismic survey further includes: afourth seismic receiver within the same receiver line, such that theseismic survey includes the plurality of seismic receivers beingpositioned within the survey area with the deliberately non-uniformspacing within the same receiver line, the deliberately non-uniformspacing including a first spacing distance between the fourth seismicreceiver and the first seismic receiver being different than a secondspacing distance between the fourth seismic receiver and the secondseismic receiver.
 5. The method of claim 3, wherein the seismic surveyfurther includes: an additional receiver line including one or moreseismic receivers of the plurality of receivers, the additional receiverline being distinct from the same receiver line and the differentreceiver line, the seismic survey including the deliberately non-uniformspacing between receiver lines, the deliberately non-uniform spacingincluding: the different receiver line being between the additionalreceiver line and the same receiver line; and the different receiverline being placed closer to the additional receiver line than to thesame receiver line.
 6. The method of claim 1, wherein the seismic surveyincludes the seismic energy being generated by a plurality of seismicsource points.
 7. The method of claim 6, wherein the plurality ofseismic source points is uniformly arranged within the survey area. 8.The method of claim 6, wherein designing the seismic survey furtherincludes: selecting a plurality of source point positions within thesurvey area at which to place the plurality of seismic source points,the plurality of source point positions including a first source pointposition for a first seismic source point of the plurality of seismicsource points and a second source point position for a second seismicsource point of the plurality of seismic source points, the plurality ofsource point positions selected such that the first source pointposition for the first seismic source point is not aligned along thefirst direction with the second source point position for the secondseismic source point.
 9. The method of claim 8, wherein the plurality ofsource point positions further includes a third source point positionfor a third seismic source point of the plurality of seismic sourcepoints, the plurality of source point positions further selected suchthat the first source point position for the first seismic source pointis not aligned along the second direction with the third source pointposition for the third seismic source point.
 10. The method of claim 1,wherein each of the plurality of positions is not randomly selected. 11.The method of claim 10, wherein an arrangement of a plurality of seismicsource points for generating the seismic energy is also not randomlyselected.
 12. The method of claim 1, wherein the plurality of positionsare selected based on one or more synthetic seismic surveys generatedusing a computer, each of the one or more synthetic seismic surveysusing a different arrangement of the plurality of seismic receivers. 13.The method of claim 12, wherein generating each of the one or moresynthetic seismic surveys includes creating a reconstructed wavefield,the reconstructed wavefield being compared to a model wavefieldrepresenting the geological subsurface.
 14. The method of claim 1,wherein a reconstructed wavefield representing the geological subsurfaceis created using the seismic data.
 15. The method of claim 14, whereinthe reconstructed wavefield is created using a statistical linearregression analysis.
 16. The method of claim 14, wherein thereconstructed wavefield is iteratively refined based on measured datafrom the seismic survey, the seismic survey being a sparse seismicsurvey.
 17. The method of claim 14, wherein the reconstructed wavefieldis created using a statistical linear regression analysis that minimizesL₀ and L₁ norms, such that the reconstructed wavefield represents anactual wavefield of the geological subsurface.
 18. The method of claim1, wherein the survey area is a marine survey area.
 19. The method ofclaim 1, wherein the survey area is a land survey area.
 20. The methodof claim 1, wherein the seismic data is obtained following the designingof the seismic survey and a deployment of the plurality of seismicreceivers within the survey area according to the seismic survey. 21.The method of claim 1, wherein the second direction is perpendicular tothe first direction.
 22. The method of claim 1, wherein the seismicsurvey is a sparse seismic survey characterized by the plurality ofseismic receivers within the survey area being less numerous than auniform arrangement of seismic receivers.